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GCSE Mathematics Problem Solving Algebra Higher Tier The curve y = x2 +2x - 15 intersects the x axis at points A and B. Find the length of the line AB? To find the length of AB you need to know the coordinates of A and B Next consider how to find the coordinates of the points A and B When the curve intersects the x-axis y = 0. Therefore, 0 = x2 +2x - 15 Solve the quadratic equation to find the values for x that satisfy the equation. 0 = x2 +2x - 15 The first step in solving this equation is to factorise. ( x + 5 )( x - 3 ) What two terms multiply to make x2 ? What two numbers multiply to make -15 and add to give + 2? x – 15 Add + 2 1 x – 15 -1 x 15 3 x -5 -3 x 5 -14 14 -2 2 0 = (x + 5)(x – 3) So, x+5=0 or x–3=0 If x+5=0 then x = -5 If x-3=0 then x = 3 A ( -5, 0) These values are the x coordinates for A and B. The y coordinates will be ‘0’ for both A and B B(3, 0) Sketch the curve y = x2 +2x – 15 to help find the length of the line AB Both points lie on the x axis, so we can see from the sketch that the distance between the points (-5,0) and (3,0) is the difference between the x coordinates. So AB is equal to 8 units.